Somewhere along the way in a math class in elementary, middle or high school, you may have encountered the idea of graphing lines and thinking about the equations that represent those lines.
We are going to try to illustrate the idea of regression analysis using some hypothetical data on runners.
Let’s think about this idea using the hypothetical example of several runners.
The orange line represents a runner who runs 6 miles every hour. In 2 hours, this person will have run 12 miles, and if that runner continued for 3 hours of running, they would run 18 miles.
We can write an equation that represents the distance run in several equivalent ways:
\(distance = 6 * time\)
\(miles = 6 * hours\)
\(y = 6 * x\)
In this case, the runner’s speed (6 miles per hour) is what we call the slope of the line. The orange runner is getting 6 miles of distance for every hour spent running. Economists sometimes talk about this idea as the “rate of return”: For every hour of running, the orange runner gets 6 miles of distance.
Imagine now two other runners, represented by a red line and a blue line.